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> A tree is still more complex than strings, because it has rules: one parent per node and no cycles. Those need to be validated.

Hmm, I'm not convinced that this is sufficient to show that strings are simpler.

After all, a string has rules too: a cell in the string is either at the beginning, or the end, or the middle, and it has neighbours left, right or not at all depending on those conditions, and at most one such neighbour in each direction. Even appeal to the physical world doesn't help. If I have a physical piece of DNA, how do I know it hasn't mutated so that two different strands branch off it and it becomes, essentially, a degenerate tree?

I do think that the thrust of your argument is correct but it's not as clear cut (at least not yet) as you seem to be making out.

> What is absoutely clear is that System F and TM are essentially, qualitatively and objectively very different

Absolutely agreed! If they weren't, I'd be happy writing my day-to-day code in Turing Machines.

You're talking about the graphical representation of a string. A string is any stream of measurements (over time, if you like).

> If they weren't, I'd be happy writing my day-to-day code in Turing Machines.

And if they weren't, we'd see neurons or DNA using type-theory!

Since you seem to have thought about the fine details of this much more than you are letting on here and on your blog post I suggest you post an addendum (or even a new blog post) to be more precise about what exactly they are. There's a lot missing as it stands, and interested readers like myself are left to fill in the blanks.

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